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Description
Simulating the deformation behavior of crystals provides fundamental insights into the mechanics of polycrystalline materials like metals and alloys. Single-crystal plasticity models, based on the crystallographic structure of a single grain and formulated through multisurface plasticity, describe this behavior as an optimization problem governed by the principle of maximum plastic dissipation and constrained by the crystal's slip systems. However, in rate-independent models, the non-uniqueness of active slip systems presents algorithmic challenges, necessitating robust, efficient methods to handle computationally demanding simulations. Conventional approaches include active set searches with regularization [1] or simplifications of the numerical problem to ensure uniqueness.
In recent years, new approaches have been developed to solve this constrained optimization problem. One of the most promising methods is the primal-dual interior-point method (PDIPM), which addresses the ill-posed nature of the problem without relying on perturbation techniques [2,3]. In PDIPM, barrier functions are used to penalize infeasible solutions. However, unlike classical penalty methods, this penalization is applied smoothly and gradually intensifies as the limit of the feasible domain is approached This contribution examines the effectiveness of PDIPM for single-crystal plasticity, focusing on primal variable selection and its impact on performance, as well as its extension to account for complex hardening functions.
[1] C. Miehe and J. Schröder. A comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity. International Journal for Numerical Methods in Engineering, 50:273–298, 2001.
[2] L. Scheunemann, P. Nigro, J. Schröder, and P. Pimenta. A novel algorithm for rate independent small strain crystal plasticity based on the infeasible primal-dual interior point method. International Journal of Plasticity, 124:1–19, 2020.
[3] E. S. Perdahcıoğlu, “A rate-independent crystal plasticity algorithm based on the interior point method,” Computer Methods in Applied Mechanics and Engineering, vol. 418, p. 116533, Jan. 2024
